Total attendance for the tournament was set to surpass 200,000 on Sunday, up from 175,000 last year, with about 10 million euros (more than $11 million) in ticket sales, up 23 percent from 2014.

With Rome bidding for the 2024 Olympics, Binaghi suggests building an entirely new tournament venue and national training center near the Leonardo Da Vinci airport, which could also be used for the games.

"It's great to dream, and link this dream to the 2024 bid, so this tournament can have the (space) that it deserves," said Carlo Mornati, vice secretary general of the Italian Olympic Committee (CONI).

The Foro Italico, built under Benito Mussolini in the 1920s and 30s, has hosted the Italian Open since 1935. A historic monument, laws prevent certain types of construction.

The tournament is run by both the federation and CONI.

The stadium was built by CONI, and Binaghi said the original plan contained an additional 2,000 to 3,000 seats, which would have made the facility much more appropriate.

There have been promises to add a roof to the stadium.

"Every year we try to invent new solutions but there's not that much more that we can do," Binaghi said, adding that he has discussed the situation with Italian Olympic Committee president Giovanni Malago.

"We have to see if we need to divorce or continue this relationship (with CONI)," Binaghi said.

Roger Federer, who lost Sunday's final to Novak Djokovic, likened the situation to those at other historic tournaments like the French Open that are also growing.

"I'm just not sure if it's always clever to go bigger and bigger and bigger," Federer said. "I think it's great that tennis is going well. I see record attendance every single week now and it's beautiful to see. But I'm just worried that if you go too big and too great that you're going to stretch what the quality of the product is going to be like.

"Maybe you're happier to be in an intimate setting like here or in Paris or Miami," Federer added. "I'm also for growth — don't get me wrong — but history is here."

Binaghi's announcement may have only been a political move, part of an ongoing feud with the city government.

"Partially it's sometimes also pressure, wanting to get rid of pressure and show politicians that, 'We're ready to move in case,'" Federer said. "But it seems like there's space here. ... So maybe they can do some stuff here."

Maria Sharapova, who won the women's tournament for the third time, pointed to the picturesque Pietrangeli court, which is surrounded by neo-classical statues.